Try not to fret over the event. Just think of it as something FUN you're going to do on September 15th. People of many different shapes, sizes and athletic abilities do Tough Mudders, Warrior Dashes, Spartan Sprints, etc...
I take it you signed the "maimed, mutilated and dismemberment clause" ? It's the document you sign or click on that acknowledges that if you are maimed, mutilated or dismembered in anyway, it's your own darned fault. I know, I had to sign one of those for the Spartan Sprint I'm doing in November.
Because of you're knee, you'll want to wear extra support to protect. You might even consider compression socks for your calves. These events can lead to some very serious injuries. So, you do have to be mindful of any injuries you already have.
As far as training, you're going to have to increase the amount of strength you do. If at all possible, lots of push ups and pull ups. Do you have a local play ground ? Many play grounds have monkey bars. There's usually a monkey bar obstacle. So, practicing on the park monkey bars will help. Burpees, do lots and lots of burpees between now and the race. My race has a 30 burpee penalty for any obstacle you miss. and I LOATHE burpees.
If any one exercise helps a get a person fit, it's burpees... and yes, I still LOATHE them. www.youtube.com/watch?v=PYfNA_lmkHM
The point ? Do what you can over the next month to increase your overall strength. Body weight exercises would be squats, lunges, burpees, push ups, pull ups, etc... If you have a local park, practice swinging on the monkey bars from rung to rung.
As a generality, there are going to be obstacles that require shimming under wire, moving through tubes, carrying heavy weights a distance, pulling a heavy weight a distance, pulling yourself up and over a wall with a rope, going over a wall without a rope, climbing a rope ladder, maybe some balance work by walking across a narrow beam, and the ever popular leap over fire.
If you look up Tough Mudder or Spartan Sprint, there are training schedules you could do for both. Most don't require a gym membership.
Be glad you're not doing the Spartan Sprint. Not only do you have to jump over the wall of fire, you have to chuck a spear at a target. And if you miss the target, 30 burpee penalty. Believe me, I'm hitting that target !!
Mostly, try to enjoy yourself. But, DO baby that knee. That means having some type of brace support on it. Compression socks are another option too.